2
sinh(iz)=sinz cosh( z)=cosz
sinh( z)= sinhz cosh( z)=coshz
sin( z)=sinhz cos( z)=coshz
i i i i i i i 2 2 1 2 1 2 1 2 1 2 1 2 1 2 cosh z sinh z =1
sinh(z +z )=sinhz coshz +coshz sinhz cosh(z +z )=coshz coshz +sinhz sinhz sinhz =sinhx cosy + coshx siny
3 2 2 2 2 2 2 2 2
sinhz =sinh x+sin y
coshz =sinh x+cos y
d tanhz =sech z dz d coshz = cosec z dz d
sechz = sechz tanhz dz
d
4 LOGARİTMİK FONKSİYONLAR w logz i 2nπ i Θ i 2nπ i Θ+2nπ z =e Þ log z = w e =z e =1 n =0,±1,±2.... z = r e e θ=Θ+2nπ (n =0,±1,±2...) z = r e Þ Þ log z = lnr+i(Θ+2nπ) arg(z)= θ
5 1 2 1 2 1 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 2
log(z z )= logz +logz
z
log = logz logz z
arg(z z )=argz +argz
8 KAYNAKLAR
Complex Variables and Applications,
J.W. Brown and R.V. Churchill, 1990.
Kısmi Diferansiyel Denklemler,
Schaum’s Outlines, P. Duchateu ve D.W. Zachmann, 2000.
Complex Analysis, Theodore W.
